In order to act righteously, it is necessary that you:
1. have given the matter sufficient thought* to reasonably conclude (Prudence):
____A. the act will benefit (on the whole) whatever person(s)/society the act concerns (Justice),
____B. that it is neither excessive nor deficient in light of the circumstances (Temperance),
_and furthermore:
2. you must overcome whatever resistance there is to actually performing the act (Fortitude).
[*Sufficient thought need not—and in many cases should not—take a significant amount of time, but as one can never act voluntarily without making some judgement about the situation, prudence is a feature of all moral action. Wisely judging the amount of deliberation that is required, is itself an act of virtue. In the case of habitual action, the deliberative thought might have been performed sometime in the past. Human acts, and hence human virtues, are extended in time.]
If an act is unwise, then it is necessarily also unjust, intemperate, and rash, and vice versa.
For example, if eating a 3rd slice of chocolate cake in one day is wrong, this can only be because careful thought (Prudence) would reveal that it is too much (Temperance) to be healthy for your body (Justice) and hence that one should resist the temptation to do so (Fortitude).
Eating 3 slices cannot both be "too many all things considered", yet still "wise to choose"; nor can it be "bad for you", yet also "admirable to continue upon encountering resistance and pain". (Except perhaps in the sense that the willpower required, could later be turned to better purposes.) And the same relation holds between every other pair of cardinal virtues.
Similarly, if an act is, of its nature, good for society (Justice), but is done at an inopportune time or in excess (lack of Temperance), this presumably implies that it would have been even better for society if it had been done in a better way. Thus, the failure of Temperance is itself also a failure of Justice, and of Prudence as well.
It is even more obvious that if you are contemplating an act which is Prudent, Just, and Temperate, but you chicken out of actually doing it, that none of the sweetness you were aiming for will actually occur.
When we state that an act involves a failure of one specific virtue, this should be understood as being advice for improvement. Since a human being cannot attend to all features of their act simultaneously, we point them to whichever feature of the act they need to be thinking about in order to act better. (Picking the wrong feature, e.g. telling a smoker about the health benefits of quitting when they are already fully aware of this, is a failure of moral rhetoric).
In some cases our best judgement turns out to be in error, yet following our best judgement is still virtue, since virtue belongs to the genus of skill, not the genus of luck. One cannot choose to be lucky, except insofar as cultivating opportunities for luck is itself a matter of skill (as e.g. the skillful card player will cultivate hands, such that a greater number of possible card draws would result in winning the game).
All four of these virtues are therefore necessary, to some degree, in every virtuous act. Just as the human body cannot survive for even an hour without any one of the 1) brain, 2) heart, or 3) lungs functioning. (Apart from artificial medical substitutes.) You need ALL of them to be working. The total failure of any one of these 3 organs, will almost immediately cause catastrophic failure of all other organs. Of course if you value survival on the order of weeks, we could add several more vital organs to this list!
Not every virtue with a name, thus contains the whole of Virtue. Some virtues (e.g. Chastity, Sobriety, Studiousness) are instead virtue as restricted to a particular subject matter. In such cases, it is of course possible to fail in one area of life, while not failing in other areas of life. So far, I have argued only that the 4 traditional cardinal virtues implicitly contain all of Virtue within them.
Are there other such virtues? If virtue can also be understood as our duty to the gods, then Piety is also the form of every virtue. But what must the gods be for this unity to make sense? (Euthyphro). First, the gods must have a unity of will among themselves; and second, the union of their will with goodness must be necessary rather than accidental. The dilemma points us towards Ethical Monotheism, not Atheism.
